Bessonov, E G

Mikhailichenko, A A

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  JUNE 5, 2001                                                                                                   CLNS 01/1745FAST COOLING OF HEAVY IONS IN A STORAGE RINGE.G. Bessonov1, A.A. MikhailichenkoCornell University, Wilson Laboratory, Ithaca, NY 14853AbstractPeculiarities of the optical stochastic cooling of ion beams in storage rings are discussed.The rate of the energy losses in magnetic field for proton and ion is many orders of magnitudeless than for electron due to the mass ratio. From the other hand, the number of the photonsemitted by particles in undulators at the first harmonic has an optimum, corresponding to theoptimal undulator field, which depends on the period of undulator, the charge and mass ofparticles and on type of undulator (plane, helical) [1]. The number of photons emitted byparticles in undulators in this case does not depend on the energy of this particles and theirsmass. Based on this observation, the effective sources of both incoherent and coherent undulatorradiation were suggested [2].So the hardness of the radiation emitted by different particles having the same relativistic factorsmight be the same if trajectory and relativistic factor are the same. The only difference mightoccur due to limitations in maximum magnetic field achievable (~105 G) so period of undulatormust be adjusted also.One of important parameters of undulators is the deflecting parameter202 cmqHKipiλ= ,                                                                 (1)where q, im  are the particle’s charge and mass respectively, 0λ  is period of the undulator, H  isthe value of magnetic field in the undulator. At the optimum fields the deflecting parameter isabout unit.The number of photons emitted by a particle on the first harmonic in the energy intervalM/1/ ≅∆ γγ εε , where M  is the number of periods, can be found as [1]22214KKcqN+≅∆hγ .                                                           (2)The last formula (2) for multi charged ions becomes22222221414KKZKKceZN+≡+≅∆ αγh,                                            (3)where ce h/2=α  is the fine structure constant, and q = Ze is the charge of ion.                                                          1 Visiting from Lebedev Physical Institute RAS, Moscow, Russia2In its turn the energy exchange between the particle and the electromagnetic wave in the planarundulator now determined by the following equationϕγλε CosKMZeEdtvEq LL 20≅=∆ ∫ rr ,                                             (4)where ϕ  is the phase location of  the particle in the electromagnetic wave, 2/ cmiεγ = .The fact that the number of the photons radiated by multi charged particle is about 2Z  timeshigher, than for single charged particle drastically improves performance of the optical stochasticcooling [3]. Really, the number of the photons in the bandwidth, emitted in the first undulator isproportional to222022222 γαγλαλααγbbbuu lLNZlMNZlMNZNZN =≅=≅ ,                              (5)where N is total number of particles in the bunch, bl  is the length of the bunch,  0λML =  is thelength of the undulator, 2021 /γλλ =u  is the wavelength of radiation.This number must overwhelm the number of the photons associated with the noise of amplifier.The last one can be made as low as a single photon in the coherence volume [4].One can see that the multi charge ions have advantage 2~ Z , if compared with single chargedparticles such as protons, electrons or muons. With other words, multi charged particle radiates2Z  more photons under the same conditions such as the same gamma factor and the sametrajectory. Together with (4) following calculations done in [3] one can obtain the formula foramplification coefficient required for laser amplifier becomes the sameNMri1εκ ≅ ,                                                              (6)where 222 / cmeZr ii =  is the classical ion radius, )/( εεγε ∆×= bl  is the normalized longitudinalemittance. Last formula gives for amplification required a factor ~ 2/1 Z in favor of multi chargedions.In addition, the emittance reduction during the cooling [3]uifNZ αεε21≅ ,                                                                   (7)where fi εε ,  are initial and final emittances respectively, becomes significantly lower in thiscase also. In the last formula (7) we neglected the number of noise photons n referred to the exitof first undulator as nNZ u ≥α2.All this opens a possibility for fast cooling of ions in a storage ring, as the number of the turns,required for decrease of betatron amplitudes and/or energy spread is equal to the number of theparticles in the bandwidth uN [5].3For single charged particles, limitation on the number particles in the bandwidth is restricted byrequirement, that the number of radiated photons in the bandwidth must be at least one. So theminimal number of the particles in the bandwidth must be at least α/1~uN .So for multi charged particles the possibility for a single turn cooling becomes open as thenumber of the photons radiated must be of order of one can be satisfied for multi chargedparticles easily, as 12 ≥αZ  for ions having 12137 ≅≥Z .In original publication [3] it was mentioned, that the method considered could be applied to anycharged particle.Examples of applications of optical stochastic cooling for heavy ions considered in [6,7] missedthis peculiarity of interaction of multi charged particles with electromagnetic wave, however.References[1] D.E. Alferov, Yu.A. Bashmakov,  E.G.Bessonov, Sov. Phys. Tech. Phys., v.18, 1974, p.1336;      D.E. Alferov, Yu.A. Bashmakov, K.A. Belovintsev, E.G. Bessonov, P.A. Cherenkov,Particle Accel.  9, 223(1979).[2] E.G.Bessonov, Free-ion lasers with radiative ion cooling, Nucl. Instr. Methods, A 358 (1995)p. 204-207.[3] A.A. Mikhailichenko, M. S. Zolotorev, Phys. Rev. Lett. 71, 4146 (1993).[4] A.E. Siegman, Lasers, (University Sciences Books, Mill Valley, CA,1986).[5] S. Van der Meer, CERN Report No. CERN/ISR PO/72-31, 1972(unpublished).[6] M. Zolotorev, A. Zholents, Phys. Rev. E 50, 3087(1994).[7] A.A. Mikhailichenko, CLNS–98-1539, 1997, 14.pp. Also in Proceeding of 20th InternationalConf. on LASERS’97, New Orleans, LA, 15-19 Dec 1997, pp. 890-897.

Fast Cooling of Heavy Ions in a Storage Ring

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